Question

Before we can make the mashed potatoes, we need to boil some water. The water starts out at room temperature, 70° F, and increases by 50° F per minute. Create a linear equation using time t (in minutes) and temperature y (in °F) that models this heating of water. How many minutes until the water boils at 212° F?

Answer 1

Part a)
`y=50t+70`

Part b)
`t=2.84\ min`

Explanation:

Part a) Create a linear equation

Let

t ----> the time in minutes

y ---> the temperature in °F

we know that

The linear equation in slope intercept form is equal to

`y=mt+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

In this problem we have

The slope m is equal to

`m=50\° F\ per\ minute`

The y-intercept is

`b=70\° F`

substitute

`y=50t+70`

Part b) How many minutes until the water boils at 212° F?

For y=212° F

substitute in the linear equation and solve for t

`212=50t+70`

`50t=212-70`

`50t=142`

`t=2.84\ min`